712 Assignment 2

Author: Marah Shahin
ID: 500055421
UPI: msha846

import numpy as np 
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import tsfresh
from IPython.display import Image
sns.set()

%matplotlib inline
%load_ext autoreload
%autoreload 2

swimDF = pd.read_csv('swimGood.csv',parse_dates=['time'],index_col=[0],header=0,names=['time','ax','ay','az','|a|'])
fbDF = pd.read_csv('passing.csv',parse_dates=['time'],index_col=[0],header=0,names=['time','ax','ay','az','|a|'])
swimDF.shape, fbDF.shape

((16172, 4), (14607, 4))

swimDF.head(), fbDF.head()

(                           ax    ay    az   |a|
 time                                           
 2020-09-23 13:41:41.704 -0.41 -0.04  0.24  0.47
 2020-09-23 13:41:41.714 -0.27  0.46 -0.17  0.55
 2020-09-23 13:41:41.725 -0.16  0.29 -0.84  0.90
 2020-09-23 13:41:41.735  0.01 -0.12 -1.09  1.09
 2020-09-23 13:41:41.745  0.06 -0.18 -0.84  0.86,
                            ax    ay    az   |a|
 time                                           
 2020-09-24 12:30:03.214 -0.22  1.23 -0.17  1.26
 2020-09-24 12:30:03.224 -0.37  0.44 -0.53  0.78
 2020-09-24 12:30:03.260 -0.34 -1.00 -0.54  1.18
 2020-09-24 12:30:03.261 -0.38 -0.80 -0.03  0.88
 2020-09-24 12:30:03.262 -0.41 -0.29  0.11  0.51)

Description of Activities

Activity 1: Swimming

The first activity was swimming. The lane was 25 metres in length and the swimming style was backstroke. The phone was mounted on the left arm facing leftward from the subject (figure below). The phone was secured vertically and the subject experienced little movement from the phone throughout the activity.

Image(filename = "meSwim.jpg")

Activity 2: Football

The next activity was football. Specifically, the subject was passing a ball back and forth for just over 2 minutes. The phone was mounted in the same location as that of the first activity to avoid unecessary differences between data collections. A snapshot of the activity and phone can be seen in the figure below.

Image(filename='meBall2.jpg')

swimDF.plot(title ='Swimming Accelerometer Signal')
fbDF.plot(title ='Football Accelerometer Signal')

<matplotlib.axes._subplots.AxesSubplot at 0x1bfd9a00>

Plot Comments

It's clear football results in an overall greater variance of magnitude throughout the activity. It's also interesting that the transition period for swimming is predominately greater than the football activity signal (possibly due to getting out of the pool, getting the band off, etc). The transition period for football is of a much smaller magnitude (a person ended the recording for me). Nevertheless, these periods are clear and will be removed in the next steps. Just manually, the signals vary in magnitude and patterns. The signals are likely to result in a solid, reliable classifying model.

# Create timeline vector
delta_tSwim = swimDF.index
delta_tSwim = delta_tSwim - delta_tSwim[0]
delta_tFB = fbDF.index
delta_tFB = delta_tFB - delta_tFB[0]
delta_tSwim, delta_tFB

(TimedeltaIndex([       '00:00:00', '00:00:00.010000', '00:00:00.021000',
                 '00:00:00.031000', '00:00:00.041000', '00:00:00.078000',
                 '00:00:00.079000', '00:00:00.080000', '00:00:00.082000',
                 '00:00:00.091000',
                 ...
                 '00:02:42.203000', '00:02:42.205000', '00:02:42.206000',
                 '00:02:42.207000', '00:02:42.217000', '00:02:42.228000',
                 '00:02:42.236000', '00:02:42.246000', '00:02:42.256000',
                 '00:02:42.266000'],
                dtype='timedelta64[ns]', name='time', length=16172, freq=None),
 TimedeltaIndex([       '00:00:00', '00:00:00.010000', '00:00:00.046000',
                 '00:00:00.047000', '00:00:00.048000', '00:00:00.050000',
                 '00:00:00.060000', '00:00:00.070000', '00:00:00.080000',
                 '00:00:00.090000',
                 ...
                 '00:02:26.449000', '00:02:26.459000', '00:02:26.469000',
                 '00:02:26.479000', '00:02:26.489000', '00:02:26.528000',
                 '00:02:26.529000', '00:02:26.530000', '00:02:26.532000',
                 '00:02:26.539000'],
                dtype='timedelta64[ns]', name='time', length=14607, freq=None))

swimDF['delta_t']=delta_tSwim
fbDF['delta_t']=delta_tFB
swimDF.head(),fbDF.head()

(                           ax    ay    az   |a|         delta_t
 time                                                           
 2020-09-23 13:41:41.704 -0.41 -0.04  0.24  0.47        00:00:00
 2020-09-23 13:41:41.714 -0.27  0.46 -0.17  0.55 00:00:00.010000
 2020-09-23 13:41:41.725 -0.16  0.29 -0.84  0.90 00:00:00.021000
 2020-09-23 13:41:41.735  0.01 -0.12 -1.09  1.09 00:00:00.031000
 2020-09-23 13:41:41.745  0.06 -0.18 -0.84  0.86 00:00:00.041000,
                            ax    ay    az   |a|         delta_t
 time                                                           
 2020-09-24 12:30:03.214 -0.22  1.23 -0.17  1.26        00:00:00
 2020-09-24 12:30:03.224 -0.37  0.44 -0.53  0.78 00:00:00.010000
 2020-09-24 12:30:03.260 -0.34 -1.00 -0.54  1.18 00:00:00.046000
 2020-09-24 12:30:03.261 -0.38 -0.80 -0.03  0.88 00:00:00.047000
 2020-09-24 12:30:03.262 -0.41 -0.29  0.11  0.51 00:00:00.048000)

Remove Transition Periods

#Swimming
swimDF['seconds'] = delta_tSwim.seconds +delta_tSwim.microseconds/1e6
swimDF2 = swimDF.reset_index()
swimDF3 = swimDF2.drop(swimDF2.index[0:40])
swimDF4 = swimDF3.drop(swimDF3.index[-2000:])
swimDF4.plot(title ='Swimming Pruned Signal', y='|a|',x='delta_t')

#Football
fbDF['seconds'] = delta_tFB.seconds +delta_tFB.microseconds/1e6
fbDF2 = fbDF.reset_index()
fbDF3 = fbDF2.drop(fbDF2.index[0:600])
fbDF4 = fbDF3.drop(fbDF3.index[-500:])
fbDF4.plot(title ='Football Pruned Signal', y='|a|',x='delta_t')

<matplotlib.axes._subplots.AxesSubplot at 0x1e9fa748>

swimDF4=swimDF4.reset_index(drop=True)
swimDF4.head()

	time	ax	ay	az	|a|	delta_t	seconds
0	2020-09-23 13:41:42.107	0.07	-0.07	-0.25	0.26	00:00:00.403000	0.403
1	2020-09-23 13:41:42.116	0.06	0.10	-0.23	0.25	00:00:00.412000	0.412
2	2020-09-23 13:41:42.126	0.00	0.26	-0.08	0.27	00:00:00.422000	0.422
3	2020-09-23 13:41:42.136	-0.02	0.20	0.04	0.20	00:00:00.432000	0.432
4	2020-09-23 13:41:42.146	-0.02	-0.06	-0.04	0.07	00:00:00.442000	0.442

fbDF4 = fbDF4.reset_index(drop=True)
fbDF4.head()

	time	ax	ay	az	|a|	delta_t	seconds
0	2020-09-24 12:30:09.233	0.78	-0.58	-3.04	3.19	00:00:06.019000	6.019
1	2020-09-24 12:30:09.243	0.79	-0.49	-3.09	3.22	00:00:06.029000	6.029
2	2020-09-24 12:30:09.283	0.81	-0.48	-3.11	3.24	00:00:06.069000	6.069
3	2020-09-24 12:30:09.285	0.85	-0.60	-3.08	3.25	00:00:06.071000	6.071
4	2020-09-24 12:30:09.286	0.86	-0.78	-3.00	3.21	00:00:06.072000	6.072

Length of signal after transition period was removed

The signals are now 142 (first sample is at 0.4s) and 135 (141-6) seconds for swimming and football activites, respectively.

Add windows

swimWindow_inx = np.asarray(np.floor(swimDF4.index/100).values,np.int)
swimWindow_inx

array([  0,   0,   0, ..., 141, 141, 141])

fbWindow_inx = np.asarray(np.floor(fbDF4.index/100).values,np.int)
fbWindow_inx

array([  0,   0,   0, ..., 135, 135, 135])

swimDF4['window_idx'] = ['s{:03}'.format(idx) for idx in swimWindow_inx]
swimDF4.tail()

	time	ax	ay	az	|a|	delta_t	seconds	window_idx
14127	2020-09-23 13:44:03.842	-0.70	0.81	-0.83	1.35	00:02:22.138000	142.138	s141
14128	2020-09-23 13:44:03.852	-0.42	0.53	-1.06	1.25	00:02:22.148000	142.148	s141
14129	2020-09-23 13:44:03.862	-0.15	0.22	-1.24	1.26	00:02:22.158000	142.158	s141
14130	2020-09-23 13:44:03.872	0.13	-0.03	-1.42	1.42	00:02:22.168000	142.168	s141
14131	2020-09-23 13:44:03.882	0.24	-0.34	-1.65	1.70	00:02:22.178000	142.178	s141

fbDF4['window_idx'] = ['fb{:03}'.format(idx) for idx in fbWindow_inx]
fbDF4.tail()

	time	ax	ay	az	|a|	delta_t	seconds	window_idx
13502	2020-09-24 12:32:24.728	-0.24	-2.63	1.42	2.99	00:02:21.514000	141.514	fb135
13503	2020-09-24 12:32:24.729	0.11	-0.70	1.58	1.73	00:02:21.515000	141.515	fb135
13504	2020-09-24 12:32:24.730	0.53	1.53	1.55	2.24	00:02:21.516000	141.516	fb135
13505	2020-09-24 12:32:24.745	0.82	3.45	1.35	3.79	00:02:21.531000	141.531	fb135
13506	2020-09-24 12:32:24.746	0.76	4.47	1.15	4.67	00:02:21.532000	141.532	fb135

swimDF4.groupby('window_idx').count()

	time	ax	ay	az	|a|	delta_t	seconds
window_idx
s000	100	100	100	100	100	100	100
s001	100	100	100	100	100	100	100
s002	100	100	100	100	100	100	100
s003	100	100	100	100	100	100	100
s004	100	100	100	100	100	100	100
...	...	...	...	...	...	...	...
s137	100	100	100	100	100	100	100
s138	100	100	100	100	100	100	100
s139	100	100	100	100	100	100	100
s140	100	100	100	100	100	100	100
s141	32	32	32	32	32	32	32

142 rows × 7 columns

fbDF4.groupby('window_idx').count()

	time	ax	ay	az	|a|	delta_t	seconds
window_idx
fb000	100	100	100	100	100	100	100
fb001	100	100	100	100	100	100	100
fb002	100	100	100	100	100	100	100
fb003	100	100	100	100	100	100	100
fb004	100	100	100	100	100	100	100
...	...	...	...	...	...	...	...
fb131	100	100	100	100	100	100	100
fb132	100	100	100	100	100	100	100
fb133	100	100	100	100	100	100	100
fb134	100	100	100	100	100	100	100
fb135	7	7	7	7	7	7	7

136 rows × 7 columns

#remove windows with less than 100 samples
swimDF5 = swimDF4.drop(swimDF4.index[-32:])
swimDF5.groupby('window_idx').count()

	time	ax	ay	az	|a|	delta_t	seconds
window_idx
s000	100	100	100	100	100	100	100
s001	100	100	100	100	100	100	100
s002	100	100	100	100	100	100	100
s003	100	100	100	100	100	100	100
s004	100	100	100	100	100	100	100
...	...	...	...	...	...	...	...
s136	100	100	100	100	100	100	100
s137	100	100	100	100	100	100	100
s138	100	100	100	100	100	100	100
s139	100	100	100	100	100	100	100
s140	100	100	100	100	100	100	100

141 rows × 7 columns

fbDF5 = fbDF4.drop(fbDF4.index[-7:])
fbDF5.groupby('window_idx').count()

	time	ax	ay	az	|a|	delta_t	seconds
window_idx
fb000	100	100	100	100	100	100	100
fb001	100	100	100	100	100	100	100
fb002	100	100	100	100	100	100	100
fb003	100	100	100	100	100	100	100
fb004	100	100	100	100	100	100	100
...	...	...	...	...	...	...	...
fb130	100	100	100	100	100	100	100
fb131	100	100	100	100	100	100	100
fb132	100	100	100	100	100	100	100
fb133	100	100	100	100	100	100	100
fb134	100	100	100	100	100	100	100

135 rows × 7 columns

#create one large dataframe
df = pd.concat([swimDF5,fbDF5],ignore_index=True)
df = df.set_index('time')
df.index.name = None
df2 = df.drop(columns=['delta_t'])
df2.head()

	ax	ay	az	|a|	seconds	window_idx
2020-09-23 13:41:42.107	0.07	-0.07	-0.25	0.26	0.403	s000
2020-09-23 13:41:42.116	0.06	0.10	-0.23	0.25	0.412	s000
2020-09-23 13:41:42.126	0.00	0.26	-0.08	0.27	0.422	s000
2020-09-23 13:41:42.136	-0.02	0.20	0.04	0.20	0.432	s000
2020-09-23 13:41:42.146	-0.02	-0.06	-0.04	0.07	0.442	s000

Number of windows in each activity

There are 141 complete (with 100 rows) windows for swimming and 135 windows for football.

Extract Features

from tsfresh.feature_extraction import extract_features

X = extract_features(df2, column_id='window_idx', column_sort='seconds')

Feature Extraction: 100%|██████████| 20/20 [00:44<00:00,  2.23s/it]

X.head()

	ax__variance_larger_than_standard_deviation	ax__has_duplicate_max	ax__has_duplicate_min	ax__has_duplicate	ax__sum_values	ax__abs_energy	ax__mean_abs_change	ax__mean_change	ax__mean_second_derivative_central	ax__median	...	|a|__fourier_entropy__bins_2	|a|__fourier_entropy__bins_3	|a|__fourier_entropy__bins_5	|a|__fourier_entropy__bins_10	|a|__fourier_entropy__bins_100	|a|__permutation_entropy__dimension_3__tau_1	|a|__permutation_entropy__dimension_4__tau_1	|a|__permutation_entropy__dimension_5__tau_1	|a|__permutation_entropy__dimension_6__tau_1	|a|__permutation_entropy__dimension_7__tau_1
fb000	1.0	0.0	0.0	1.0	-94.81	477.9639	0.313131	-0.034343	0.001429	-0.840	...	0.223718	0.319026	0.413917	0.612670	1.383152	1.248731	1.818217	2.329479	2.793903	3.215116
fb001	1.0	0.0	0.0	1.0	-108.94	968.7772	0.576465	0.033838	0.003265	-0.465	...	0.096509	0.192626	0.192626	0.356468	0.919223	1.295477	1.970640	2.634906	3.208433	3.720443
fb002	1.0	0.0	0.0	1.0	37.79	664.0563	0.529394	-0.031414	-0.003622	0.595	...	0.274921	0.386735	0.537786	0.827416	1.577573	1.207890	1.754074	2.316838	2.881776	3.301884
fb003	1.0	0.0	0.0	1.0	-12.44	983.4576	0.576364	0.030909	0.004286	-1.055	...	0.165443	0.192626	0.288342	0.383650	0.973848	1.345547	2.005534	2.667043	3.240872	3.722407
fb004	1.0	0.0	0.0	1.0	-12.01	1158.7785	0.401414	-0.039394	0.002806	0.685	...	0.165443	0.329286	0.451359	0.668811	1.164305	1.220558	1.795744	2.294986	2.750332	3.092134

5 rows × 3136 columns

X.shape

(276, 3136)

Feature Matrix Attributes

The X feature matrix has a shape of 276 rows × 3136 columns with 3136 features extracted as per the number of columns in the 'X' dataframe above

#creat bool column for which activity is football and which is swimming
g = df2.groupby('window_idx')
windows=[]
TF = []
for name,group in g:
    windows.append(name)
    TF.append('s' in name)
d = {'window_idx': windows, 'col2': TF} #create dictionary
y = pd.DataFrame(data=d, index = windows) #create dataframe
y2 = y.drop(['window_idx'],axis=1)
y2.index.name = 'window_idx'
y3 = y2['col2']
y3

window_idx
fb000    False
fb001    False
fb002    False
fb003    False
fb004    False
         ...  
s136      True
s137      True
s138      True
s139      True
s140      True
Name: col2, Length: 276, dtype: bool

from tsfresh.transformers import FeatureSelector
select = FeatureSelector()
select.fit(X.dropna(axis=1), y3)

FeatureSelector()

Only choose most important features

select.relevant_features

attr_"abs"__coeff_39',
 'ay__fft_coefficient__attr_"abs"__coeff_40',
 'az__fft_coefficient__attr_"abs"__coeff_14',
 'ay__fft_coefficient__attr_"abs"__coeff_31',
 'az__fft_coefficient__attr_"abs"__coeff_10',
 'az__quantile__q_0.1',
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 'az__spkt_welch_density__coeff_5',
 'az__fft_coefficient__attr_"abs"__coeff_6',
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 'az__fft_coefficient__attr_"abs"__coeff_2',
 'az__fft_coefficient__attr_"abs"__coeff_5',
 '|a|__spkt_welch_density__coeff_8',
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 'ay__spkt_welch_density__coeff_5',
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 'ay__variance_larger_than_standard_deviation',
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 'ax__fft_coefficient__attr_"abs"__coeff_23',
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 'az__spkt_welch_density__coeff_8',
 'az__fft_coefficient__attr_"abs"__coeff_18',
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 'ax__spkt_welch_density__coeff_8',
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 '|a|__fft_coefficient__attr_"abs"__coeff_40',
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 'ax__fft_coefficient__attr_"abs"__coeff_13',
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 'ay__ar_coefficient__coeff_3__k_10',
 '|a|__fft_coefficient__attr_"abs"__coeff_36',
 '|a|__fft_coefficient__attr_"abs"__coeff_32',
 '|a|__fft_coefficient__attr_"abs"__coeff_35',
 '|a|__fft_coefficient__attr_"abs"__coeff_34',
 '|a|__fft_coefficient__attr_"abs"__coeff_37',
 'ax__quantile__q_0.8',
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 'az__agg_linear_trend__attr_"intercept"__chunk_len_50__f_agg_"min"',
 'ax__fft_coefficient__attr_"abs"__coeff_37',
 '|a|__fft_coefficient__attr_"abs"__coeff_44',
 'az__fft_coefficient__attr_"abs"__coeff_19',
 '|a|__fft_coefficient__attr_"abs"__coeff_41',
 'az__quantile__q_0.2',
 '|a|__spkt_welch_density__coeff_2',
 'ax__fft_coefficient__attr_"abs"__coeff_38',
 'ax__fft_coefficient__attr_"abs"__coeff_0',
 'az__fft_coefficient__attr_"abs"__coeff_32',
 '|a|__cwt_coefficients__coeff_14__w_20__widths_(2, 5, 10, 20)',
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 'az__fft_coefficient__attr_"abs"__coeff_26',
 'ax__fft_coefficient__attr_"abs"__coeff_32',
 '|a|__fft_coefficient__attr_"abs"__coeff_47',
 'ax__fft_coefficient__attr_"abs"__coeff_40',
 'az__fft_coefficient__attr_"abs"__coeff_1',
 '|a|__cwt_coefficients__coeff_13__w_20__widths_(2, 5, 10, 20)',
 'ax__fft_coefficient__attr_"abs"__coeff_39',
 'ax__spkt_welch_density__coeff_2',
 'az__fft_coefficient__attr_"abs"__coeff_34',
 'ax__fft_coefficient__attr_"abs"__coeff_31',
 'az__fft_coefficient__attr_"abs"__coeff_30',
 '|a|__fft_coefficient__attr_"abs"__coeff_48',
 'az__fft_coefficient__attr_"abs"__coeff_28',
 '|a|__fft_coefficient__attr_"abs"__coeff_49',
 'ax__quantile__q_0.3',
 'az__fft_coefficient__attr_"abs"__coeff_37',
 'ax__fft_coefficient__attr_"abs"__coeff_42',
 'az__fft_coefficient__attr_"abs"__coeff_22',
 '|a|__fft_coefficient__attr_"abs"__coeff_46',
 '|a|__cwt_coefficients__coeff_12__w_20__widths_(2, 5, 10, 20)',
 'az__fft_coefficient__attr_"abs"__coeff_36',
 'az__fft_coefficient__attr_"abs"__coeff_35',
 'ax__fft_coefficient__attr_"abs"__coeff_44',
 'ax__fft_coefficient__attr_"abs"__coeff_41',
 'ax__fft_coefficient__attr_"abs"__coeff_43',
 'az__fft_coefficient__attr_"abs"__coeff_24',
 'ax__fft_coefficient__attr_"abs"__coeff_46',
 'az__fft_coefficient__attr_"abs"__coeff_31',
 '|a|__cwt_coefficients__coeff_11__w_20__widths_(2, 5, 10, 20)',
 'az__number_crossing_m__m_1',
 'az__fft_coefficient__attr_"abs"__coeff_25',
 'az__fft_coefficient__attr_"abs"__coeff_38',
 'ax__fft_coefficient__attr_"abs"__coeff_47',
 'ax__fft_coefficient__attr_"abs"__coeff_48',
 '|a|__cwt_coefficients__coeff_5__w_5__widths_(2, 5, 10, 20)',
 'az__fft_coefficient__attr_"abs"__coeff_29',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"var"',
 '|a|__ar_coefficient__coeff_4__k_10',
 'ax__fft_coefficient__attr_"abs"__coeff_49',
 'az__fft_coefficient__attr_"abs"__coeff_40',
 '|a|__cwt_coefficients__coeff_2__w_2__widths_(2, 5, 10, 20)',
 'ay__ar_coefficient__coeff_5__k_10',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"var"',
 '|a|__cwt_coefficients__coeff_10__w_20__widths_(2, 5, 10, 20)',
 'az__fft_coefficient__attr_"abs"__coeff_39',
 'ax__fft_coefficient__attr_"abs"__coeff_45',
 'az__fft_coefficient__attr_"abs"__coeff_46',
 'az__fft_coefficient__attr_"abs"__coeff_43',
 'ay__number_crossing_m__m_1',
 '|a|__cwt_coefficients__coeff_11__w_10__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_10__w_10__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_6__w_5__widths_(2, 5, 10, 20)',
 'ax__fft_coefficient__attr_"abs"__coeff_2',
 '|a|__cwt_coefficients__coeff_12__w_10__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_9__w_10__widths_(2, 5, 10, 20)',
 'az__fft_coefficient__attr_"abs"__coeff_42',
 '|a|__ar_coefficient__coeff_3__k_10',
 '|a|__cwt_coefficients__coeff_4__w_5__widths_(2, 5, 10, 20)',
 'az__quantile__q_0.3',
 'az__fft_coefficient__attr_"abs"__coeff_47',
 'az__fft_coefficient__attr_"abs"__coeff_45',
 'az__fft_coefficient__attr_"abs"__coeff_44',
 '|a|__cwt_coefficients__coeff_8__w_10__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_7__w_10__widths_(2, 5, 10, 20)',
 'ax__fft_coefficient__attr_"abs"__coeff_50',
 'ay__fft_coefficient__attr_"abs"__coeff_0',
 '|a|__cwt_coefficients__coeff_9__w_20__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_6__w_10__widths_(2, 5, 10, 20)',
 'az__fft_coefficient__attr_"abs"__coeff_49',
 'az__fft_coefficient__attr_"abs"__coeff_48',
 'ax__ar_coefficient__coeff_4__k_10',
 '|a|__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"var"',
 'az__fft_coefficient__attr_"abs"__coeff_41',
 'ax__number_crossing_m__m_-1',
 '|a|__cwt_coefficients__coeff_13__w_10__widths_(2, 5, 10, 20)',
 '|a|__fft_coefficient__attr_"abs"__coeff_50',
 '|a|__cwt_coefficients__coeff_8__w_20__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_3__w_2__widths_(2, 5, 10, 20)',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"var"',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"var"',
 'az__number_crossing_m__m_-1',
 '|a|__cwt_coefficients__coeff_5__w_10__widths_(2, 5, 10, 20)',
 'ax__ar_coefficient__coeff_3__k_10',
 'az__fft_coefficient__attr_"abs"__coeff_50',
 '|a|__cwt_coefficients__coeff_1__w_2__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_7__w_20__widths_(2, 5, 10, 20)',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"max"',
 'ay__ar_coefficient__coeff_2__k_10',
 '|a|__cwt_coefficients__coeff_14__w_10__widths_(2, 5, 10, 20)',
 '|a|__benford_correlation',
 '|a|__cwt_coefficients__coeff_7__w_5__widths_(2, 5, 10, 20)',
 '|a|__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"var"',
 'az__fft_coefficient__attr_"abs"__coeff_0',
 'ax__variance_larger_than_standard_deviation',
 'ay__number_crossing_m__m_-1',
 '|a|__cwt_coefficients__coeff_6__w_20__widths_(2, 5, 10, 20)',
 '|a|__cwt_coefficients__coeff_3__w_5__widths_(2, 5, 10, 20)',
 'ay__ar_coefficient__coeff_6__k_10',
 'ay__quantile__q_0.4',
 'az__quantile__q_0.7',
 '|a|__cid_ce__normalize_True',
 '|a|__cwt_coefficients__coeff_4__w_10__widths_(2, 5, 10, 20)',
 'ay__c3__lag_1',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"min"',
 'ax__quantile__q_0.7',
 '|a|__autocorrelation__lag_2',
 '|a|__cwt_coefficients__coeff_5__w_20__widths_(2, 5, 10, 20)',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"var"',
 'ay__skewness',
 '|a|__partial_autocorrelation__lag_1',
 '|a|__autocorrelation__lag_1',
 'ax__number_crossing_m__m_1',
 '|a|__cwt_coefficients__coeff_4__w_20__widths_(2, 5, 10, 20)',
 '|a|__ar_coefficient__coeff_5__k_10',
 '|a|__autocorrelation__lag_3',
 '|a|__fft_aggregated__aggtype_"skew"',
 'ay__time_reversal_asymmetry_statistic__lag_3',
 'ax__ar_coefficient__coeff_2__k_10',
 'ax__quantile__q_0.4',
 'ay__ar_coefficient__coeff_7__k_10',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"var"',
 '|a|__large_standard_deviation__r_0.2',
 '|a|__cwt_coefficients__coeff_3__w_20__widths_(2, 5, 10, 20)',
 'ax__ar_coefficient__coeff_5__k_10',
 'az__quantile__q_0.4',
 '|a|__cwt_coefficients__coeff_3__w_10__widths_(2, 5, 10, 20)',
 'ay__quantile__q_0.6',
 '|a|__cwt_coefficients__coeff_4__w_2__widths_(2, 5, 10, 20)',
 '|a|__ar_coefficient__coeff_2__k_10',
 'az__ar_coefficient__coeff_2__k_10',
 '|a|__fft_aggregated__aggtype_"kurtosis"',
 '|a|__cwt_coefficients__coeff_8__w_5__widths_(2, 5, 10, 20)',
 '|a|__autocorrelation__lag_4',
 '|a|__value_count__value_1',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"min"',
 '|a|__cwt_coefficients__coeff_2__w_20__widths_(2, 5, 10, 20)',
 'ay__count_above_mean',
 'ay__count_below_mean',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"max"',
 'ax__cid_ce__normalize_True',
 'ay__time_reversal_asymmetry_statistic__lag_2',
 '|a|__ratio_beyond_r_sigma__r_3',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"max"',
 '|a|__cwt_coefficients__coeff_2__w_5__widths_(2, 5, 10, 20)',
 '|a|__fourier_entropy__bins_100',
 'ay__augmented_dickey_fuller__attr_"usedlag"__autolag_"AIC"',
 '|a|__fft_aggregated__aggtype_"centroid"',
 'az__ar_coefficient__coeff_3__k_10',
 '|a|__binned_entropy__max_bins_10',
 'ay__fft_aggregated__aggtype_"skew"',
 'ay__ar_coefficient__coeff_8__k_10',
 'ax__ar_coefficient__coeff_6__k_10',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.6',
 'ax__autocorrelation__lag_7',
 'ax__ar_coefficient__coeff_1__k_10',
 'az__skewness',
 'ax__autocorrelation__lag_6',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"max"',
 'ax__autocorrelation__lag_8',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.8',
 'ax__autocorrelation__lag_5',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_10__f_agg_"min"',
 '|a|__kurtosis',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.4',
 'az__longest_strike_above_mean',
 '|a|__longest_strike_above_mean',
 'az__ar_coefficient__coeff_1__k_10',
 'ax__autocorrelation__lag_4',
 'ax__autocorrelation__lag_9',
 'ay__cid_ce__normalize_True',
 'az__cid_ce__normalize_True',
 '|a|__ar_coefficient__coeff_6__k_10',
 'ax__autocorrelation__lag_3',
 'ay__fft_aggregated__aggtype_"centroid"',
 '|a|__autocorrelation__lag_5',
 'ay__number_peaks__n_1',
 'ax__autocorrelation__lag_2',
 '|a|__cwt_coefficients__coeff_2__w_10__widths_(2, 5, 10, 20)',
 'az__count_below_mean',
 'az__count_above_mean',
 '|a|__partial_autocorrelation__lag_3',
 'ay__autocorrelation__lag_1',
 'ay__partial_autocorrelation__lag_1',
 '|a|__cwt_coefficients__coeff_1__w_20__widths_(2, 5, 10, 20)',
 'ay__lempel_ziv_complexity__bins_10',
 'ay__ar_coefficient__coeff_10__k_10',
 '|a|__agg_autocorrelation__f_agg_"var"__maxlag_40',
 'ay__approximate_entropy__m_2__r_0.3',
 'ay__ratio_beyond_r_sigma__r_3',
 'ax__number_peaks__n_10',
 'ay__value_count__value_0',
 'ay__fft_coefficient__attr_"angle"__coeff_0',
 'az__autocorrelation__lag_3',
 'az__autocorrelation__lag_2',
 'ay__ar_coefficient__coeff_1__k_10',
 'ay__autocorrelation__lag_2',
 'ay__binned_entropy__max_bins_10',
 'ay__number_peaks__n_3',
 'az__permutation_entropy__dimension_3__tau_1',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.2',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.6__ql_0.2',
 'ay__partial_autocorrelation__lag_3',
 'ay__fourier_entropy__bins_100',
 '|a|__partial_autocorrelation__lag_4',
 'az__number_cwt_peaks__n_1',
 '|a|__large_standard_deviation__r_0.25',
 'az__autocorrelation__lag_4',
 'ay__ar_coefficient__coeff_9__k_10',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.6',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.6__ql_0.4',
 'az__ar_coefficient__coeff_5__k_10',
 '|a|__autocorrelation__lag_6',
 'az__ar_coefficient__coeff_4__k_10',
 'az__permutation_entropy__dimension_4__tau_1',
 '|a|__augmented_dickey_fuller__attr_"usedlag"__autolag_"AIC"',
 'ax__fourier_entropy__bins_100',
 'ax__approximate_entropy__m_2__r_0.9',
 'az__autocorrelation__lag_5',
 '|a|__ratio_beyond_r_sigma__r_1',
 'ax__ar_coefficient__coeff_7__k_10',
 'ax__value_count__value_0',
 'ay__partial_autocorrelation__lag_2',
 'ax__partial_autocorrelation__lag_1',
 'ax__autocorrelation__lag_1',
 'ay__number_cwt_peaks__n_1',
 'az__autocorrelation__lag_6',
 'az__autocorrelation__lag_1',
 'az__partial_autocorrelation__lag_1',
 '|a|__number_peaks__n_3',
 '|a|__skewness',
 'ax__fourier_entropy__bins_10',
 'az__autocorrelation__lag_7',
 'ay__time_reversal_asymmetry_statistic__lag_1',
 '|a|__cwt_coefficients__coeff_9__w_5__widths_(2, 5, 10, 20)',
 'az__value_count__value_0',
 '|a|__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.2',
 '|a|__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.4',
 'az__autocorrelation__lag_8',
 'az__approximate_entropy__m_2__r_0.9',
 'ax__agg_autocorrelation__f_agg_"var"__maxlag_40',
 '|a|__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.8',
 'az__autocorrelation__lag_9',
 'ay__c3__lag_2',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"min"',
 '|a|__autocorrelation__lag_7',
 '|a|__ratio_beyond_r_sigma__r_2.5',
 'ay__autocorrelation__lag_3',
 'ay__fourier_entropy__bins_3',
 '|a|__ratio_beyond_r_sigma__r_1.5',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"min"',
 'ax__number_cwt_peaks__n_1',
 'ay__approximate_entropy__m_2__r_0.5',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.6__ql_0.2',
 '|a|__lempel_ziv_complexity__bins_5',
 '|a|__sum_of_reoccurring_values',
 'ay__sum_values',
 'ay__mean',
 'ay__fft_coefficient__attr_"real"__coeff_0',
 'az__permutation_entropy__dimension_5__tau_1',
 'ay__sample_entropy',
 'az__approximate_entropy__m_2__r_0.7',
 '|a|__lempel_ziv_complexity__bins_10',
 'az__c3__lag_1',
 'az__time_reversal_asymmetry_statistic__lag_3',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.4__ql_0.2',
 'az__fourier_entropy__bins_100',
 '|a|__cwt_coefficients__coeff_0__w_20__widths_(2, 5, 10, 20)',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.6',
 'ax__fft_coefficient__attr_"real"__coeff_0',
 'ax__sum_values',
 'ax__mean',
 'ay__number_peaks__n_5',
 'ay__has_duplicate_max',
 'az__ar_coefficient__coeff_6__k_10',
 '|a|__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.6',
 'ay__cwt_coefficients__coeff_8__w_2__widths_(2, 5, 10, 20)',
 '|a|__ar_coefficient__coeff_7__k_10',
 'ax__approximate_entropy__m_2__r_0.7',
 '|a|__number_peaks__n_5',
 'ay__ratio_beyond_r_sigma__r_1.5',
 '|a|__partial_autocorrelation__lag_2',
 '|a|__autocorrelation__lag_8',
 'ax__benford_correlation',
 'ay__fourier_entropy__bins_2',
 'az__fft_coefficient__attr_"angle"__coeff_0',
 'ax__ratio_beyond_r_sigma__r_3',
 'ay__ar_coefficient__coeff_0__k_10',
 'ay__fft_aggregated__aggtype_"kurtosis"',
 '|a|__lempel_ziv_complexity__bins_100',
 'ay__large_standard_deviation__r_0.2',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.4',
 '|a|__fft_aggregated__aggtype_"variance"',
 'ay__lempel_ziv_complexity__bins_100',
 '|a|__autocorrelation__lag_9',
 'ay__lempel_ziv_complexity__bins_5',
 'ay__benford_correlation',
 '|a|__approximate_entropy__m_2__r_0.9',
 '|a|__change_quantiles__f_agg_"mean"__isabs_False__qh_0.6__ql_0.2',
 '|a|__fourier_entropy__bins_10',
 'ay__cwt_coefficients__coeff_5__w_2__widths_(2, 5, 10, 20)',
 'az__fft_aggregated__aggtype_"centroid"',
 'ax__fourier_entropy__bins_5',
 'az__median',
 'ay__cwt_coefficients__coeff_9__w_2__widths_(2, 5, 10, 20)',
 'ax__fourier_entropy__bins_3',
 'az__ratio_beyond_r_sigma__r_3',
 '|a|__cwt_coefficients__coeff_1__w_10__widths_(2, 5, 10, 20)',
 'az__permutation_entropy__dimension_6__tau_1',
 'az__fft_aggregated__aggtype_"skew"',
 'ay__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.0',
 'ay__variation_coefficient',
 '|a|__cwt_coefficients__coeff_1__w_5__widths_(2, 5, 10, 20)',
 'ay__cwt_coefficients__coeff_7__w_2__widths_(2, 5, 10, 20)',
 'ay__agg_linear_trend__attr_"intercept"__chunk_len_50__f_agg_"mean"',
 'ax__ratio_beyond_r_sigma__r_1.5',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"max"',
 '|a|__sum_of_reoccurring_data_points',
 'ax__c3__lag_3',
 'az__approximate_entropy__m_2__r_0.5',
 'ay__has_duplicate',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.4__ql_0.2',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.6__ql_0.4',
 'ay__cwt_coefficients__coeff_6__w_2__widths_(2, 5, 10, 20)',
 'ay__kurtosis',
 'az__number_peaks__n_3',
 'az__approximate_entropy__m_2__r_0.1',
 'ax__fft_coefficient__attr_"imag"__coeff_1',
 '|a|__cwt_coefficients__coeff_10__w_5__widths_(2, 5, 10, 20)',
 'ax__median',
 'ay__lempel_ziv_complexity__bins_3',
 'az__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"max"',
 'az__number_crossing_m__m_0',
 'az__number_peaks__n_5',
 'ay__ratio_beyond_r_sigma__r_2.5',
 'ax__approximate_entropy__m_2__r_0.5',
 'ay__number_cwt_peaks__n_5',
 'az__time_reversal_asymmetry_statistic__lag_2',
 'az__change_quantiles__f_agg_"mean"__isabs_False__qh_0.8__ql_0.2',
 'ax__agg_linear_trend__attr_"intercept"__chunk_len_5__f_agg_"min"',
 'ay__autocorrelation__lag_9',
 'ax__ar_coefficient__coeff_0__k_10',
 'az__has_duplicate_max',
 'ax__ar_coefficient__coeff_8__k_10',
 'ay__value_count__value_1',
 'ay__autocorrelation__lag_4',
 'ay__fft_aggregated__aggtype_"variance"',
 'ax__agg_linear_trend__attr_"rvalue"__chunk_len_10__f_agg_"min"',
 'ax__ratio_beyond_r_sigma__r_2.5']

p_values = pd.Series(select.p_values, index= select.features)
p_values[select.relevant_features]

|a|__fft_coefficient__attr_"real"__coeff_0                        9.581794e-47
|a|__mean                                                         9.581794e-47
|a|__fft_coefficient__attr_"abs"__coeff_0                         9.581794e-47
|a|__sum_values                                                   9.581794e-47
|a|__abs_energy                                                   1.045313e-46
                                                                      ...     
ay__value_count__value_1                                          1.916598e-03
ay__autocorrelation__lag_4                                        2.004167e-03
ay__fft_aggregated__aggtype_"variance"                            2.024619e-03
ax__agg_linear_trend__attr_"rvalue"__chunk_len_10__f_agg_"min"    2.076591e-03
ax__ratio_beyond_r_sigma__r_2.5                                   2.152619e-03
Length: 841, dtype: float64

select.relevant_features[:5]

['|a|__fft_coefficient__attr_"real"__coeff_0',
 '|a|__mean',
 '|a|__fft_coefficient__attr_"abs"__coeff_0',
 '|a|__sum_values',
 '|a|__abs_energy']

from sklearn.ensemble import RandomForestClassifier
# Random forest
clf = RandomForestClassifier(max_features=5)
clf.fit(X[select.relevant_features], y3)

RandomForestClassifier(max_features=5)

from sklearn.pipeline import make_pipeline

model = make_pipeline(FeatureSelector(), RandomForestClassifier())

Repeated Cross-validation

from sklearn.model_selection import RepeatedKFold

kf = RepeatedKFold(n_splits=10, n_repeats=10)

Xd = X.dropna(axis=1)
predictions = list()
truth = list()
for train, test in kf.split(Xd):
    model.fit(Xd.iloc[train], y3.iloc[train])
    predictions.append(model.predict_proba(Xd.iloc[test]))
    truth.append(y3.iloc[test])

from sklearn.model_selection import cross_val_score
scores = cross_val_score(clf, Xd, y3, cv=kf, scoring='roc_auc')
scores

array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

Scores do not vary with changes in test and training sets. Hence, the model does not appear overfit.

p = np.concatenate(predictions)
t = np.concatenate(truth)
p.shape, t.shape

((2760, 2), (2760,))

from sklearn.metrics import roc_curve, roc_auc_score

fpr, tpr, thresholds = roc_curve(t, p[:,1])

plt.plot(fpr, tpr)

[<matplotlib.lines.Line2D at 0x257cce08>]

roc_auc_score(t,p[:,1])

0.9999259259259259

The score is very close to 1.0 therefore, this is a very good classifier.

Visualising Important Features

Xi = X[['|a|__fft_coefficient__attr_"real"__coeff_0','|a|__mean','|a|__fft_coefficient__attr_"abs"__coeff_0','|a|__sum_values','|a|__abs_energy']]
Xi["activity"] = y3
sns.pairplot(Xi,hue = "activity") #where true is swimming

<seaborn.axisgrid.PairGrid at 0x24e42aa8>

Pair plot comments

The orange and blue dots are reasonably distinct in the majority of the plots. This could explain why the model does well in distinguishing between the two signals.

Extract minimal set of features

visualising some common features

from tsfresh.feature_extraction.settings import MinimalFCParameters

minimal_fc = MinimalFCParameters()

minimal = sorted(minimal_fc.keys())
minimal

['length',
 'maximum',
 'mean',
 'median',
 'minimum',
 'standard_deviation',
 'sum_values',
 'variance']

minimal_fc

{'sum_values': None,
 'median': None,
 'mean': None,
 'length': None,
 'standard_deviation': None,
 'variance': None,
 'maximum': None,
 'minimum': None}

mod_minimal_fc = minimal_fc.copy()

del mod_minimal_fc['standard_deviation']

mod_minimal_fc

{'sum_values': None,
 'median': None,
 'mean': None,
 'length': None,
 'variance': None,
 'maximum': None,
 'minimum': None}

#check out JUST |a| signal
df3 = df2.drop(['ax','az','ay'],axis=1)
df3.head()

	|a|	seconds	window_idx
2020-09-23 13:41:42.107	0.26	0.403	s000
2020-09-23 13:41:42.116	0.25	0.412	s000
2020-09-23 13:41:42.126	0.27	0.422	s000
2020-09-23 13:41:42.136	0.20	0.432	s000
2020-09-23 13:41:42.146	0.07	0.442	s000

X4 = extract_features(df3, column_id='window_idx', column_sort='seconds', default_fc_parameters=mod_minimal_fc)

Feature Extraction: 100%|██████████| 20/20 [00:02<00:00,  9.01it/s]

X4.head()

	|a|__sum_values	|a|__median	|a|__mean	|a|__length	|a|__variance	|a|__maximum	|a|__minimum
fb000	309.44	2.910	3.0944	100.0	1.350395	7.89	0.63
fb001	575.17	5.205	5.7517	100.0	12.327392	14.23	0.71
fb002	824.87	7.555	8.2487	100.0	15.486413	23.30	1.44
fb003	591.43	5.450	5.9143	100.0	8.962543	13.73	1.35
fb004	427.34	3.780	4.2734	100.0	9.798202	21.34	0.95

X4["activity"] = y3
sns.pairplot(X4,hue = "activity") #where true is swimming

<seaborn.axisgrid.PairGrid at 0x1bf95fe8>

Pair plot comments

The orange and blue dots are reasonably distinct in the majority of the plots. This could explain why the model does well in distinguishing between the two signals.